Method and Apparatus for Optical Waveguide-to-Semiconductor Coupling for Integrated Photonic Circuits

ABSTRACT

A grating coupler couples a waveguide to a beam and is formed of patterned shapes in a first and second layer of planar material, the shapes embedded in background material, the layers separated by less than one wavelength. The shapes are organized as a plurality of adjacent unit cells arranged along a direction of propagation of light with each unit cell including a shape of the first material and a shape of the second material, each unit cell having design parameters including a period, a width wb of the shape of first planar material, a width wt of the shape of second planar material, and an offset between the shapes. The coupler has a directivity ratio D is at least 10 dB between “up” and “down” radiation; and unit cells differ in at least one parameter selected from period, wb, wt, and offset to provide a predetermined beam shape.

PRIORITY CLAIM

The present document claims priority to U.S. Provisional PatentApplication 62/311,358 filed 21 Mar. 2016, and U.S. Provisional PatentApplication 62/311,355 filed 21 Mar. 2016. The entirety of theaforementioned patent applications are incorporated herein by reference.

GOVERNMENT INTEREST

This invention was made with government support under grant numberHR0011-11-C-0100 awarded by DOD/DARPA, and ECCS1128709 awarded byNational Science Foundation. The government has certain rights in theinvention.

TECHNICAL FIELD

The present document relates to the field of integrated circuits havingintegrated optical devices and, in many embodiments, electronic deviceson the same die. In particular embodiments, the integrated opticaldevices include optical waveguides and other optical components on asame die as CMOS circuitry.

BACKGROUND

There are many applications, including cameras, optical datatransmitters, and optical data receivers, where electronic circuitry andoptical devices are combined on a single integrated circuit.

It is also widely known that a significant limitation of modernprocessors and system-on-a-chip design is data transfer betweenfunctional units on a very large-scale integrated (VLSI) circuit; wheredistributed resistance and capacitance of interconnect may significantlylimit data rates. An electro-optical interconnect may help solve thislimitation on data rates. Further, many VLSI-based system designs sufferlimitations on data rate due to the resistance of bondpad drivers andcapacitance of chip-to-chip interconnect; electro-optical interconnectsmay prove a solution to this problem also. Furthermore, the energy perbit transferred of electronic interconnects may place a power budgetlimitation on the operation of an electronic microchip. Electro-opticalinterconnects may enable lower energy per bit interconnects. Finally,electrical interconnects may incur electrical cross-talk betweenadjacent wire lines that limits the spatial bandwidth density ofinterconnection to/from a chip. Optical interconnects may employ densewavelength division multiplexing (DWDM) to achieve orders of magnitudehigher bandwidth density without incurring significant cross-talkpenalties.

Integrated photonics, including silicon photonics, has potential toenable electronic-photonic circuits with advanced optical signalprocessing functions and capabilities. One important area of applicationis energy-efficient photonic links for processor to memory chipcommunication, as well as chip-to-chip and on-chip interconnects. Otherapplications include active optical cables for rack-to-rackinterconnects, transmitters and receivers for 100 Gbps Ethernet andbeyond, as well as applications such as sensing, imaging (e.g. opticalcoherence tomography, etc.) and image/video projection applications,beam steering, and visible light biophotonic chips for high throughputbiotechnology applications.

Integrated and silicon photonics typically employ customized fabricationprocesses. For silicon photonics, this typically means usingsilicon-on-insulator (SOI) wafers with a thick-oxide thickness of 2-3microns, and materials and/or lithography and process steps that aretailored to photonics, these process modifications are not compatiblewith high density microelectronics.

Microelectronics, on the other hand, relies on carefully optimizedcomplementary metal oxide semiconductor (CMOS) processes, such as thoseused for microprocessors and dynamic random access memory (DRAM) chips.Key potential applications for photonic integrated circuits includecommunications between state of the art CMOS logic chips includingmicroprocessors and DRAM memory chips; optical interfaces to networkprocessing chips, as well as other aspects of communications systems andmixed electronic-optical signal processing chips. CMOS-SOI (CMOSprocesses using silicon on insulator substrates) processes that includetransistors usually are also optimized for microelectronics. Exceptionsare SOI silicon photonics processes which usually do not supporttransistor integration, especially not advanced-node (e.g. sub 65 nm)transistors.

Efficient optical fiber to on-chip waveguide coupling, and photonic viasfor chip to chip, die to die, or layer to layer communication within achip/die, are also desirable in photonic chips with applications incommunications, cameras, and other devices fabricated using CMOS andCMOS-SOI electronics processes (examples including GlobalFoundries GFUS45RFSOI and 12SOI 45 nm and 32SOI 32 nm SOI processes, and e.g. 10LPe 65nm bulk CMOS (all formerly IBM)), as well as custom photonics (e.g. IMECISIPP50G, LETI and IHP as accessible e.g. through the Europractice ICportal; AIM Photonics Institute (Albany, N.Y.) Passives and Activessilicon photonics processes as of this writing, IME Singapore, andothers), and custom electronics-photonics processes (such as processesco-developed by Luxtera, Inc. and Freescale).

Three-dimensional (3D) die stacking results in chips having multiple diebonded together. An example is the Hybrid Memory Cube (HMC) (Trademarkof Hybrid Memory Cube Consortium, Beaverton, Oreg.) technology forstacked memory chips. Electrical power and communication between dies inthe stack may be done off-chip via wire bonding, or using throughsilicon vias (TSVs). Optical interconnection between device layers ofseveral stacked die chips may prove an alternative to electricalinterconnections.

SUMMARY

A grating coupler couples a waveguide to a beam and is formed ofpatterned shapes in a first and second device layer of planar material,the shapes embedded in background material, the layers separated by lessthan one wavelength. The shapes are organized as a plurality of adjacentunit cells arranged along a direction of propagation of light with eachunit cell including a shape of the first material and a shape of thesecond material, each unit cell having design parameters including aperiod, a width wb of the shape of first planar material, a width wt ofthe shape of second planar material, and an offset in the plane betweenthe shapes. The coupler has a directivity ratio D of least 10 dB between“up” and “down” radiation; and unit cells differ in at least oneparameter selected from period, wb, wt, and offset to provide apredetermined beam shape.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic cross section diagram of a PRIOR ART deviceproduced using a modern CMOS SOI process, including a MOSFET transistorcross-section.

FIG. 2 is a schematic cross section of a PRIOR ART device produced witha modern bulk CMOS fabrication process including a MOSFET transistorcross-section.

FIG. 3 shows a top view layout of two grating couplers connected by awaveguide, each grating coupler having a grating (also referred to as a“grating array”), and a waveguide taper to transform the guided modefrom a small cross-section waveguide to the width of the grating.

FIG. 4 is a schematic cross-section of a portion of a PRIOR ART gratingarray, illustrating a non-uniform grating structure formed ofpartial-thickness cuts of constant depth and varying widths, defined bya lithographic mask, into a top surface of a core material (such assilicon) waveguide layer.

FIGS. 5-8 are example top view chip layout views of grating couplershaving transverse segmentation in some grating bars formed on apolysilicon layer.

FIG. 9 shows an example top view chip layout of a grating coupler whichdoes not use transverse segmentation in the waveguide taper section.

FIG. 10 illustrates how constructive interference in a two-elementscattering unit can direct power up, while destructive interferenceensures that little or none is radiated down.

FIGS. 11A, 11B, 11C, and 11D illustrates directional radiation from atwo-scatterer unit cell with quarter-wavelength spacing in the verticaland horizontal direction, the scatterers being positive refractive indexperturbations. In FIGS. 11A and 11B, a plane wave from the leftconstructively interferes up (FIG. 11A), and destructively downward(FIG. 11B). With the order of the scatterers switched, the radiationinterferes constructively down (FIG. 11D) and destructively up (FIG.11D).

FIGS. 12A, 12B, 12C, and 12D illustrates directional radiation from atwo-scatterer unit cell with quarter-wavelength spacing in the verticaland horizontal direction, the scatterers being negative refractive indexperturbations. In FIGS. 12A and 12B, a plane wave from the leftconstructively interferes up (FIG. 12A), and destructively downward(FIG. 12B). With the order of the scatterers switched, the radiationinterferes constructively down (FIG. 12D) and destructively up (FIG.12D).

FIGS. 13A-D illustrates directional radiation from a two-scatterer unitcell with quarter-wavelength spacing in the vertical and horizontaldirection, and one scatterer being a positive index perturbation whilethe other scatterer being a negative index perturbation. In FIGS. 13Aand 13C, a plane wave from the left constructively interferes up, anddestructively downward in FIGS. 13B and 13D. With the order of thescatterers switched, the radiation interferes constructively down anddestructively up.

FIG. 14B is a schematic cross-section illustration showing 3 unit cellsof a non-uniform grating structure, showing the four parameters thatparametrize a unit cell in this example geometry.

FIG. 14A shows a desired Gaussian beam field distribution along thegrating, the derived desired scattering strength vs. position along thegrating, and the actual grating strength synthesized using the hereinproposed method.

FIG. 15A shows the scattering strength, α, of a unit cell in the up/downoutput radiation direction of interest (in this case down) plotted vs.layer widths ratio r=wt/wb, and fill factor f=wb/Λ, with period Λ andoffset wo selected at each point to fix the output angle at the targetoutput angle value (here 20°) and maximize directivity. Designwavelength is 1200 nm.

FIG. 15B shows the directivity of a unit cell plotted vs. layer ratior=wt/wb, and fill factor f=wb/Λ, with period Λ and offset wo selected tofix the output angle (20°) and maximize directivity. Design wavelengthis 1200 nm.

FIGS. 15C and 15D provide the corresponding period Λ and layer offsetwo, respectively, for each point, defined by the coordinates(r,f)=(layer ratio, fill factor), in the scattering strength plot ofFIG. 15A and directivity plot in FIG. 15B.

FIG. 15E shows the same information as FIG. 15A, with the addition of awhite contour added to highlight the maximum directivity ridge for easyviewing, and exemplary design points A1-A3, B1-B3, C1-C3 and D1-D3included.

FIG. 15F shows the same information as FIG. 15B, with the addition of awhite contour added to highlight the maximum directivity ridge for easyviewing.

FIG. 15G shows the same information as FIG. 15C, with the addition of awhite contour added to highlight the maximum directivity ridge for easyviewing.

FIG. 15H shows the same information as FIG. 15D, with the addition of awhite contour added to highlight the maximum directivity ridge for easyviewing.

FIGS. 16A-E illustrate a Type A (Normal) synthesized grating designaccording to an embodiment of the invention, showing in FIG. 16A astructure cross-section, simulated field distribution in FIG. 16B,desired and designed beam shape in FIG. 16C, an top plan view opticalmicrograph of a fabricated device in FIG. 16D, and spectral response ofdirectivity, coupling efficiency, and reflection back to waveguide inputport in FIG. 16E; as well as the measured efficiency of a fabricateddevice for comparison. Waveguide port excitation is shown.

FIGS. 17A-E illustrate a Type B (Inverted) synthesized grating designaccording to another embodiment of the invention, showing the structurecross-section in FIG. 17A, simulated field distribution in FIG. 17B,desired and designed beam shape in FIG. 17C, an optical top plan viewmicrograph of the device in FIG. 17D, and spectral response ofdirectivity, coupling efficiency, and reflection back to waveguide inputport in FIG. 17E; as well as the measured efficiency of a fabricateddevice for comparison. Waveguide port excitation is shown.

FIG. 18 shows a 3D rendering of an example grating coupler, here Type B(Inverted), according to the described invention.

FIG. 19 shows the directivity of a unit cell plotted vs. layer ratior=wt/wb, and fill factor f=wb/A, with period, Λ, and offset, wo,selected to fix the output angle at 20° and maximize directivity.Operating wavelength is 1200 nm in this example. Four fundamental typesof grating coupler design are shown in this plot as four corners of an Xshaped “directivity ridge”. Note that a large region providesdirectivities D over 100 (i.e. 20 dB) and reaching as high as 10,000.

FIG. 20 is a simplified block diagram of a method for designing agrating coupler having high directivity.

FIGS. 21A, 21B, and 21C together are a detailed block diagram of analternative method for designing a grating coupler having highdirectivity.

FIG. 22A shows a schematic cross-section of the same structure as FIG.16A and indicates locations of three zoom-in regions.

FIGS. 22B, 22C and 22D show magnified regions of the structure of FIG.22A.

FIG. 23A shows a schematic cross-section of the structure of FIG. 17Aand indicates locations of two magnified regions.

FIGS. 23B and 23C show magnified regions of the structure in FIG. 23A.

DETAILED DESCRIPTION OF THE EMBODIMENTS

We provide an optical coupler adapted to radiate a unidirectional beamof a desired field distribution shape in the beam cross-section, whichin some embodiments is a Gaussian field distribution, from an in-planeguided wave excitation on an optical or optoelectronic integratedcircuit chip. Radiation out of plane is provided by the “array antenna”behavior of a grating structure as shown in FIGS. 3-9. FIG. 3 is a topplan view of a grating coupler assembly such as may be used for testing.This structure has a first coupler with a grating 100 and a taperstructure 102 that may receive in incident beam and couple light into awaveguide 104. Waveguide 104 feeds light into a second coupler havingtaper structure 106 and thence to grating 108. FIG. 4 illustrates aportion of grating 108.

In the grating structures shown in FIGS. 3-9, in-plane guided wave lightincident on the array can be thought, in the weak perturbation picture,to produce a polarization current in each perturbation to the uniform(z-invariant) waveguide structure, within each grating gap or bar.Grating bars may also be referred to as grating teeth. Grating bars mayhave a uniform cross-section across a transverse waveguide width (in thedirection normal to the cross-section such as the one shown in FIG.14B). Grating bars may also be curved in the transverse direction.Whether straight or curved, grating bars may be segmented, perforated orotherwise patterned in the transverse direction by the same mask thatdefines the bar width (horizontal width of bar in a cross-sectional viewsuch as FIG. 14B). Such segmentation, perforation or patterning mayserve as an alternative parameter to modulating bar width to control thescattering strength of the unit call. Such a parameter may besubstituted for wt of the top bar width or wb of bottom bar width in thegrating coupler designs provided here. Either the top, bottom or bothsets of bars may include some transverse segmentation, perforation orpatterning.

The array of grating bars with associated polarization currents(currents due to perturbation of a guided wave by index changes thatchange a uniform waveguide cross-section into the grating) acts like aphased array antenna and radiates in the direction in which the elementsare in phase. In a conventional grating coupler patterned in a singledevice layer with symmetry about a plane passing through the plane ofthe waveguide circuit, the grating radiation pattern is exactlysymmetric for output radiation into the up and down directionsperpendicular to a plane of the grating bars and the waveguide circuit.Even for a grating coupler that does not have a perfect symmetry about aplane passing through the plane of the waveguide circuit, but ispatterned by a single mask, often there is likewise approximately asymmetric radiation pattern, depending on the material layer stack. Thissymmetry limits efficiency of radiating into one beam above or below thechip to about 50% (−3 dB), since the other 50% of incident power goes inthe opposite direction. Another 1 dB of loss in uniformly periodicstructures can be attributed to the mode mismatch between theexponential radiated field and the Gaussian fiber mode or other targetbeam shape. To break this up/down symmetry, previous work has usedvarious approaches including metallic or dielectric stack mirrorsintegrated into the device, and required additional processing steps tobe integrated into the photonic chip, or required more expensive, customspecialty silicon and/or silicon-on-insulator wafers with dielectricmirrors, which add to processing costs and complexity.

An exemplary embodiment of a prior art structure that has approximatelysymmetric radiation pattern, and thus shows poor directivity isillustrated in FIG. 4. Such gratings typically offer fiber-chip couplingloss of 3-4 dB at the design wavelength. In FIG. 4, a single siliconwaveguide-core layer 120 is illustrated having a grating ofpartial-thickness cuts 122 formed into its upper surface.Partial-thickness cuts, whether in an arbitrary dielectric (e.g. siliconnitride), polysilicon or crystalline silicon device layers such assilicon photonic waveguide cores or active transistor layers sometimesalso utilized as waveguide core material, require additional processingsteps and complexity including usually a timed etch. In particular,partial etch steps are not supported in standard CMOS or CMOS-SOIprocessing. Thus, a design not requiring partial etches is additionallyadvantageous for monolithic CMOS and CMOS-SOI integration, and providesmore robust designs in other platforms because it does not rely on theaccuracy of realization of a partial etch depth.

In general, grating couplers disclosed herein comprise a grating couplerstructure comprising an array of scattering unit cells, a waveguideport, and a beam port. The waveguide port is in-plane and typicallyformed in one or more of the device layers used to form the gratingcoupler structure, and can be used as an input or output. The beam portis above the grating coupler for devices designed to couple to upwardradiation, and below the grating coupler for devices designed to coupleto downward radiation. The beam port may interface with an optical fibermode of an abutted optical fiber or fiber array, or may be an opticalbeam mode that traverses a distance in air or background materials priorto coupling to an optical fiber or interfacing to another opticaldevice.

In an embodiment of the invention, we replace each element of thegrating by a pair of “scatterers”, the two scatterers forming a unitcell and the unit cells forming an array that may be periodic,quasi-periodic or not periodic. We first consider the case of a periodicarray, although the inventive embodiments specifically call for anaperiodic array. We consider the periodic array, because the propertiesof a single unit call can be understood by considering it as part of aninfinite array—and those properties utilized to synthesize an optimalaperiodic array. Thus, we break the design into two parts—an arraypattern (periodic array) and an element pattern (the two scatterersinside a single unit cell). The radiation from the complete periodicarray of such unit cells can be thought of as the multiplication ofthese two radiation patterns (radiation vs. angle) or convolution inspace. The unit cell is shown in FIG. 10, where the two weak scatterersare separated in a quarter wavelength (effective wavelength in theheterogeneous medium of scatterer material and background material(s))in both the horizontal (co-planar with multiple scatterers in the samematerial layer) and vertical (perpendicular to the plane defined bymultiple scatterers in the same material layer) directions. Then, when aplane wave is incident from the left (FIG. 10), scattered lightcoherently adds in the up direction, and destructively interferes in thedown direction. Thus, we obtain an element pattern with little or nolight radiated in a downward direction. Since the linear array patternwill have two main lobes of interest symmetrically about the plane inwhich the array lies (one in each of the upward and downward directions,at an angle off-normal selected by design), ideally the element null inthe downward direction will be in the direction of the main lobe for anupward radiating design. Thus, it cancels the (e.g.) downward radiationand allows only upward radiation. The converse also works, where theelement pattern nulls out the upward main lobe, thus favoring downwardradiation. We have used this to show nearly 100% directivity in designsusing only a pair of patternable device layers.

Similar structures can be made to operate with vertical spacing otherthan a quarter wavelength vertical spacing between the two layers ofweak scatterers, however other design parameters, including horizontaloffset between shapes of the two layers, may require adjustment forappropriate function. Here, the quarter wavelength spacing refers to thewavelength in the medium, equal to the free-space wavelength divided bythe refractive index. In a weakly scattering structure, the refractiveindex of the background medium or material stack and scatterers may besimilar so this wavelength in the medium is well defined. In the case ofstrong scatterers, the refractive index of the scatterers and thebackground medium or materials in a background material stack, maydiffer substantially, i.e. have high index contrast. Low index contrast(weak scattering) may be considered <1% index change. High indexcontrast refers to refractive index differences between one index andanother that represent small turn radii for waveguides, and tightconfinement in the cross-section on the sub-wavelength scale of thewavelength in the core material. Material system examples includesilicon nitride (SiN) core with silica cladding (n=1.9 or 2.4 core andn=1.45 cladding), silicon with silica (3.5:1.45) or silicon nitride(3.5:2.0) cladding. In other words, high index contrast typically refersto 10% or greater difference between refractive indices and often50-200% relative index difference. (For purposes of our designs we willfurther restrict this definition, below.) In this case, the wavelengthin the medium inside the grating is not well defined. An approximationcan be made by taking an average permittivity (square index) of themedium, weighted by the electric field distribution (index where lightis thereby having higher weighting). However, such approximations willin general provide approximations. Nevertheless, the vertical spacing ofan “effective” quarter wavelength is what defines the vertical distancebetween the two patternable device layers, and is on the order of thewavelength or less. In such a particular embodiment, vertical spacingbetween the scatterers is less than one wavelength λ of the light.

Because our designs also require scatterers in the vertical directionspaced by an effective quarter wavelength, and hence waveguides withapproximately a critical angle of the waves inside the core above 45degrees to allow similar horizontal and vertical length scales forinterference, this limits the refractive index contrast of interestfurther. With critical angle for optical reflection under obliqueincidence defined as θc=arcsin(ncladding/ncore) with ncore and ncladdingthe high and low refractive indices of the waveguide wall, for a 45°angle, an index contrast ncore/ncladding above 1.41, or above 41% isneeded. Thus, for a silica cladding of 1.45, core indices abovencore=1.45×1.41=2.05 are preferable for the grating formation.Furthermore, since a grating is partially core material and partiallycladding, there is also low index cladding material, which suggests evenhigher preferable core indices. The guided waveguide mode at the gratingcoupler input and within the grating may also need to be considerablybelow the critical angle to provide strong confinement, another reasonto aim for core materials that provide even higher critical angle, i.e.index. This means preferable materials for the two layers are silicon(crystalline or polycrystalline), and potentially high index dielectricssuch as silicon rich silicon nitride and silicon carbide that can haveindex as high as 2.4, and III-V materials. Materials with lower coreindex may provide some aspects of the suggested functions but at reducedperformance. Hence, by high index and high index contrast we willtypically refer to materials above 2.05 to 2.4 refractive index, andmore preferably above 2.4, when surrounded by silica cladding (n=1.45),and corresponding fractional index contrasts in other materialbackgrounds.

Efficient Couplers

However, this does not solve the problem of forming a Gaussian beam atthe same time as ensuring directional radiation. The challenge isnontrivial because beamforming—whether a Gaussian beam or anotherdesired beam shape—requires control by design of the scattering strengthof the elements of the grating array along the array as a function ofposition. Gratings that radiate in a single direction, and changestrength along the propagation direction without altering the angle ofradiation, are nontrivial to design. State of the art techniques involveusing brute force global optimization, such as genetic algorithms. Thesetechniques require large computational power, and have yielded couplerswith efficiency limited to 1 to 2 dB even in the best cases reported,obtained after years of improvements, and worse (3-5 dB) in common usein silicon photonics.

If one is to approach 100% efficiency, and combat both thedirectionality and the mode matching problem simultaneously, it isnecessary to create a “tapered grating” structure that can emit atailored (e.g. Gaussian) beam shape, but also employs the unidirectionalelement designs in FIG. 10. This means, in the ideal scenario, varyingscattering strength, while simultaneously maintaining a fixed outputradiation angle, and high directivity. To reduce scattering strength,the scatterers may be reduced in size. To maintain radiation direction,their relative position (owing to changes in effective index that comefrom their change in size) must change. To maintain directivity,likewise their relative position must maintain an element pattern nullon the undesired array main lobe direction. In general there are manydegrees of freedom in design, 3, 4 or more per unit cell, times thenumber of unit cells since the grating is not uniform. These degrees offreedom include thicknesses of each of the silicon layers, (vertical)layer spacing, widths of upper and lower scattering elements in eachunit cell, the offsets of upper relative to lower scattering elements ineach unit cell, and local pitch of the unit cells (i.e. full width ofeach unit cell). A second common-mode offset of the upper and lowerscattering elements in the horizontal direction relative to the unitcell may also be utilized.

We provide herein a rigorous, systematic approach and designs of highefficiency couplers that accomplish these requirements.

Before we consider this design method for high efficiency couplers, weillustrate three different situations of scatterers, which provide novelgrating coupler designs, i.e. embodiments of the invention. In FIG.11A-D, we show scatterers that have a higher refractive index (darkblocks) than the background material. Thus, after scattering there is nophase shift (aside from the 90degree phase due to the polarizationcurrent term that is always present). Thus, in FIGS. 11A and 11B, anexemplary plane wave incident from the left produces scattering thatconstructively interferes up (FIG. 11A), and destructively downward(FIG. 11B). If we switch the order of the scatterers in this gratingunit cell cross-section in relation to the input port, as in FIG. 11Cand FIG. 11D, then the radiation now interferes constructively down(FIG. 11D) and destructively up (FIG. 11D). Thus, construction accordingto FIGS. 11A and 11B gives an upward radiating grating coupler, whileFIGS. 11C and 11D gives a downward radiating one, simply by placing thetop element behind or in front of the bottom element with respect to theinput port.

In a second situation (FIG. 12), if the scatterers are lower refractiveindex (white blocks) than the background material, the same happensbecause each scatterer now provides a 180 degree phase shift uponreradiation (radiation off the scatterers), but since all scatterers dothe same, the radiation pattern is the same and there is just an overall180 degree phase delay/advance in the wave.

In a third situation (FIG. 13A-E), one scatterer in the unit cell has ahigher refractive index than background, and the other a lower one. Inthis case, the radiation direction changes from up to down or thereverse, because only one element gives an extra 180 degree phase shiftto the radiation it scatters, so the direction that previously hadconstructive interference now has destructive, and the direction thatwas previously destructively interfering is now constructivelyinterfering. Thus, FIGS. 13C and 13D show that the same scattererorientation provides radiation down whereas FIGS. 11A, 11B, 12A, and 12Bprovided radiation up, and FIGS. 11C, 11D, 12C, and 12D the conversewith radiation down.

In general, scatterers are perturbations, so if the grating unit cell,in comparison to the unperturbed waveguide, has a region of materialwhere index is increased, such as a region of oxide in the waveguidechanged to silicon, showing as an extra thickness of silicon material ontop of the waveguide forming a grating, this is a positive indexperturbation, and another region where index is decreased, such as anetched out silicon trench replaced by silica, the index perturbation isnegative. We will employ these guidelines to provide efficient designsof simultaneously unidirectional and beamforming (i.e. custom beamshape) couplers for different waveguide geometries.

This document describes on-chip, waveguide excited, out-of-plane beamformers that are formed from two device layers. These may be silicon, oranother material or combination of materials. The key property is thatthey provide scattering that is controllable by design from one unitcell to another. Since silicon has a high refractive index and scattersstrongly when surrounded by silica, and is a common photonic integratedcircuit material, we use it as the example system. To form thedirectional array element, we utilize two patterned device layers. Thisis commonly present in CMOS SOI electronics processes, as shown in FIG.1, using the gate and body layers of the transistor; and in certainsilicon photonics processes (e.g. IMEC's ISIPP50G silicon photonicsprocess supports a polysilicon device layer atop a crystalline silicondevice layer, although they are at present not independentlypatternable). We form a unit cell of the grating from a patterned shapein each of the two device layers, which we will call the top and bottomsilicon layers. The patterned shapes in the top and bottom siliconlayers we will refer to as the top and bottom silicon shapes. Moregenerally, any two high refractive index materials relative to thesurrounding background index may be used for the top and bottom devicelayers, and the top and bottom high-index shapes, per our previousguidelines on what constitutes high refractive index contrast. In CMOSSOI technology, one may use the polycrystalline gate silicon layer andthe crystalline transistor body silicon layer. We note that device layerthicknesses and vertical spacing of the device layers is a single set ofthree parameters that is typically shared by all unit cells, andpatterning of lateral dimensions allows cell to cell variation bydesign. To design the grating, we need to control the scatteringstrength of each of the top and bottom silicon shapes, their relativespacing (offset), and the local periodicity of the (usually smoothly)varying grating structure. The “joint scattering strength”, or totalradiation of the upper and lower scattering elements in each unit cell,determines the local radiation strength of the unit cell of the grating.The top shape and bottom shape are adjusted, e.g. in width, to controleffective scattering strength of each, and their strength difference isadjusted to perfectly null radiation in a certain direction. Theirrelative position offset in part controls that direction. Finally thelocal period (width of the unit cell) controls the direction of the main(wanted) beam of radiation—due to the array pattern. This pictureprovides an intuitive explanation, but is based on perturbation theorythat assumes small perturbations. In high index contrast, such assilicon photonics, rigorous numerical simulations are required to findthe dimensions needed to accomplish these goals. This is needed forreasons that include that high index contrast necessitates accountingfor multiple scattering, i.e. scattering off a first element which thenscatters off a second (and possibly back, etc.), while weak scattering,which is where perturbation theory is valid, nominally disregards ofsuch higher order effects.

In embodiments presented here, two high index material layers of similarrefractive index and thickness are used (both silicon, both 50-100 nmthick in the present example), in order to allow equal scattering fromthe two shapes in the unit cell—one in each of the top and bottomlayers—the equal scattering permitting destructive interference and thushigh directivity of a unit cell. Material layers of lower refractiveindex than silicon may be used, but high index well above 2.05-2.4 isneeded for high performance due to the quarter-wave interference in bothdirections. Different refractive indices of the two material layers maybe utilized, and compensated by differences in thickness. However,materials of too low a refractive index will result in low directivity.Using two silicon layers, we show directivities of unit cells up to10000:1 (FIG. 15B, 15F), several orders of magnitude higher thanpreviously demonstrated.

FIG. 14B shows an example embodiment of the invention, a schematic crosssection of a grating with three full unit cells. This particularstructure is envisioned as being fabricated in a CMOS SOI process, with2 silicon layers (shown in black) serving as scatterers. After thematerial stack—including layer thicknesses and material propertiesincluding refractive indices—is chosen for the entire structure (commonto all unit cells), there are 4 degrees of freedom that controllithographically each unit cell—the widths of the top and bottom siliconshapes of the unit cell, their relative translation or offset, and theunit cell size, i.e. local width or period Λ of the structure. In lieuof widths of top and bottom silicon shapes, or in addition, the shapesmay be segmented, perforated or patterned in the direction transverse tothe input waveguide (i.e. out of plane to the cross-section, such asFIG. 14B).

A Gaussian desired profile (or another desired beam shape) (Taillaert,Peter Bienstman, and Roel Baets, “Compact efficient broadband gratingcoupler for silicon-on-insulator waveguides,” Opt. Lett. 29, 2749-2751(2004)), provides the desired scattering strength α(x) vs. positionalong the grating. The designer's job is to find the 4 parameters abovefor each unit cell to realize that scattering strength distribution tothe degree possible, while maintaining the radiation angle and highdirectivity.

In one embodiment of the invention, we provide a grating coupler formedby two device layers, each device layer defining scatterers as shown inFIG. 14B in each unit cell, where the grating coupler's 4 unit cellparameters are tapered so that the scattering strength forms a Gaussianbeam, or desired beam shape, but a high directionality is maintained atall times within the grating by design of the local unit cell. Forgrating couplers intended to emit planar phase front beams, such as fornear fiber to chip coupling, the unit cells also maintain a constantangle of emission. For emission of a focusing or defocusing beam, theangle of emission is tapered along the grating to engineer the emissionphase front in addition to the intensity profile. The directiontransverse to the input waveguide in the plane of the device layer, i.e.out of plane of the cross-section such as FIG. 14B, provides atransverse beam shape that is roughly the shape of the input waveguidemode entering the grating, or approximately the width of the grating ata point along the grating where scattering out of radiation is highest,i.e. the peak power emissions point and beam center. This beam shapetypically has a good match to a Gaussian beam (a typical number is 98%),and incurs minimal mismatch loss (˜0.1 dB). Finally, any air-silicainterfaces in matching to fiber can be alleviated using index matchingfluid to fill gaps, as is done in some other fiber mating approaches.

Beam Parameters

For Gaussian beams, beam power drops off to each side of a central beamaxis. For purposes of this document, Mode Field Diameter (MFD) is, for aGaussian beam, the width between two points on opposite sides of thebeam axis at which electric field strength of the beam drops from acentral peak-power value to 1/e times the peak power value. The beamangle θ is the angle, relative to a perpendicular to the plane definedby the scatterers, at which the central beam axis leaves the coupler.The point at which the central beam axis intersects the plane defined bythe scatterers of a grating coupler is the peak power emissions point ofthe grating coupler. The beam angle θ is positive if the beam axisleaves the coupler upward or downward heading away from the inputwaveguide; negative if the beam axis leaves the coupler upward ordownward heading toward the input waveguide; and zero if the beam issurface normal.

In a focusing-beam embodiment, portions of the coupler adjacent thewaveguide have a beam angle θ1 greater than one and approximately twodegrees different than the beam angle θ2 of portions of the couplerfurthest from the waveguide to produce a converging beam that can, inprinciple, focus on an end of an optical fiber, another coupler, or on afixed point in space above/below the grating surface. In a particularfocusing-beam embodiment, a third cell at the coupler center has anominal beam angle midway between θ1 and θ2 with a uniform tapering ofnominal beam angle across the coupler. Such an embodiment may produce afocusing shaped beam, such as a Gaussian beam, by having the third cellprovide stronger scattering than a first and a second unit cell that arein the the portions with beam angle θ1 and beam angle θ2, respectively.This is in addition to providing the third unit cell with highdirectivity, along with high directivity in the portions with beam angleθ1 and beam angle θ2.

Designing the Grating

A method for synthesizing a structure that emits a simultaneouslyunidirectional and tailored beam shape beam (in particular, e.g.Gaussian) consists of the following. We use a rigorous photonic bandstructure solver that is capable of taking in a real frequency(corresponding to a free-space wavelength) and outputting acomplex-propagation-constant (momentum) eigenvalue. The solver mustsupport radiation absorbing boundary conditions (one option beingperfectly matched layers). A suitable band structure solver has beenreported in Finite-difference complex-wavevector band structure solverfor analysis and design of periodic radiative microphotonic structuresby Jelena Notaros and Milo{hacek over (s)} A. Popović, Optics Letters,Mar. 15, 2015/Vol. 40, No. 6. This solver is based on afinite-difference method on a split Yee grid. Input to the solver is adescription of the structure to be simulated (refractive indexdistribution of the cross-section of a unit cell, and frequency i.e.free-space wavelength of operation) and output is the complex wavevectorand field distribution in the unit cell. Notably, modes are computedeven in bandgaps, which traditional band solvers, with wavevector input,exclude. This is one possible solver, and other types can be utilizedthat provide the same or similar information, including the typedescribed in G. Lecamp, J. P. Hugonin, and P. Lalanne, “Theoretical andcomputational concepts for periodic optical waveguides,” Opt. Express15, 11042-11060 (2007). Since these solvers use Bloch-Floquet typeboundary conditions to solve Maxwell's equations over a unit cell of thestructure in order to solve for optical modes of periodic structures,they may be referred to as Bloch mode solvers.

To set the stage for a design, the target operating wavelength, materialstack including layer thicknesses and refractive indices at the targetwavelength, output beam angle, and desired direction of exiting beam (upor down), are selected. A variable unit cell with four parameters ischosen that vary the scattering strength of the top and bottom shape,their offset (wo) and the local period Λ (which is equivalent to unitcell width, but corresponds to period in a special case when unit cellsare identical and the array is periodic). In this example, we selectonly silicon shape width control for the top (wt) and bottom (wb) shapescattering strength design, but other options are possible as describedelsewhere in this disclosure.

The band solver is used to compute the scattering strength, a, thedirectionality, D (a ratio of power radiated up divided by powerradiated down), and primary off-normal output radiation angle, θ, in aunit cell. We obtain these three variables as a h directivities functionof the 4-dimensional space (w_(t), w_(b), w_(o) and Λ; see FIG. 14B),storing them in a 4D database for a practical range of values for eachof the 4 parameters w_(t), w_(b), w_(o) and Λ. Our approach is to firstchoose a target output beam angle for the coupler design, and eliminateall points in the 4D database that do not provide that angle. Thisreduces the design space to 3 dimensional, and the period Λ can now be adependent parameter, i.e. it can be computed for any choice of the other3 parameters such that the angle is the target beam angle. Next, foreach w_(t) and w_(b), we choose that offset w_(o) which maximizes thedirectionality D of the unit cell. Directionality D is defined as theratio of radiated power up and radiated power down from the unit cell.Radiated power up is the total Poynting power flux (in watts for a 3Dunit cell or watts/m for a 2D unit cell) in the upward direction acrossthe top surface of the unit cell, while radiated power down is the totalPoynting power flux in the downward direction across the bottom surfaceof the unit cell. Directivity D is maximized in the selected beamemission direction per specification. For each set of wt and wb, aparticular wo provides the highest D, and now we are left with a 2dimensional space (wt and wb). For a more natural representation of thedata, in our synthesis method, we then recast w_(t) and w_(b) in termsof a fill factor, f=w_(b)/Λ, and a ratio of layer widths, r=w_(t)/w_(b).We can now plot the radiation strength and the directivity vs. theremaining two parameters, f and r (FIGS. 15A, 15B, 15E, and 15F). Wenote that D for a particular unit cell may reach 10000 (10000:1) inparts of the plot showing very high D but D's in the 10 to 1000 rangealso may also provide good performance. Therefore, although optimumdirectivity is obtained along the white contours indicated in FIGS.15E,-15H for this example, there is a large area of FIG. 15B and FIG.15F that provides directivity above 1000 and an even larger one above100. Thus significant latitude is permitted in design. However, a chosencontour in FIG. 15B determines a one-dimensional line along which wt andwb are chosen to obtain particular scattering strength α(x), and thecorresponding wo and Λ are predetermined (in FIGS. 15C/15G and 15D/15H,respectively). In most embodiments of the invention, D of a unit cell isgreater than 10:1, that is 10 dB, but most designs reach 13-20 db (95:5to 99:1) and the highest performance designs reach D's well above 1000:1and up to above 10000:1 (see FIGS. 15B and 15F).

Such high directivities allow grating couplers with overall high devicedirectivity to be achieved without the need to use bottom mirrors, oreven small partial reflections off the buried oxide-silicon waferinterface, a common technique in silicon photonics to reflect additionallight to constructively interfere with up radiated light and slightlyimprove efficiency. There are several downsides of such techniques.First, they are very sensitive on the thickness of the buried oxideseparating the grating coupler device layer(s) and the silicon wafer.Since this thickness can be 2-3 microns, its uncertainty can be several10's to 100 nm, which can provide significant inefficiency. Furthermore,if there is error in the grating coupler beam output angle due toin-plane dimensional fabrication variations (over/under etch, refractiveindex error, device layer thickness error, etc.), with a new outputangle a bottom mirror approach can provide significant efficiency loss.Finally, there exist approaches to monolithic integration of siliconphotonics with advanced CMOS node microelectronics (J. S. Orcutt, etal., “Open foundry platform for high-performance electronic-photonicintegration,” Opt. Express 20, 12222-12232 (2012)) that call for theremoval of the silicon substrate in photonic device regions, and thatmay utilize grating couplers coupling light to fiber downward toward thesubstrate (i.e. in the direction where there used to be a substratebefore removal). In this case, the partial mirror at the substrateinterface lacks the silicon substrate and is weak (air-silica interface)or non-existent in the case index matching is used. Therefore, with highdirectivity unit cells with D>10 dB, and up to 20-40 dB as shown inFIGS. 15B and 15F, grating couplers can be designed that utilize onlythe device layers to achieve near unity coupling efficiency. Theadvantage is that patterning and thickness of device layers are amongthe best controlled steps in semiconductor fabrication processes, andcan provide the benefit of robust realization of the design.

High directivity occurs in an approximately X shaped region in FIG. 15B(and, better shown in FIG. 19). The maximum directivity occurs alongcontour lines, marked by wide white contour lines on FIGS. 15E and 15Fand by points A1-A3 and B1-B3, or the white contour lines and pointsA1-A3 and B1-B3 on FIGS. 15G and 15H. FIGS. 15A and 15E shows thatscattering strength varies for different choices of r and f, i.e. wt andwb, along each contour line, while directivity is high and output angleis fixed. For any choice of r and f, wt and wb are directly computed,and FIGS. 15C, 15G 15D, and 15H provide the corresponding offset wo andperiod Λ, thus completely specifying the unit cell. Therefore, we canchoose to use any part of the “X” shaped region providing a high enoughdirectivity that spans all the scattering strength values needed to forma beam, e.g. the Gaussian in FIG. 14A, by selecting points along acontour in the X shaped region to produce desired emission strength ateach point along the coupler. For the highest directivity, the white“high directivity ridge” contour as shown in FIGS. 15E-15H is used toselect the scattering strength values.

Furthermore, the “high directivity ridge” contours in FIGS. 15E-15H showthat there are four possible design types that allow a range ofscattering parameters that will permit beam shape synthesis as desired.We call the top right and top left branches of the X shaped highdirectivity ridge, in FIGS. 15B and 15F, respectively the Type A: Normaldesigns and Type B: Inverted designs (see also FIG. 19). FIG. 19 showsthere are in general four possible designs, the other two being Type C:Inverted #2 designs, and Type D: Free designs.

Referring to our discussion of types of pairs of perturbation in theunit cell in FIGS. 11A to 13D, we can classify these four types ofdesigns by looking at the axes of the plot, which are “Layer ratio”, r,and “Fill Factor”, f Low fill factor f close to 0 means (since f=wb/Λ)we have a narrow silicon shape and thus mostly oxide in the bottomdevice layer rather than silicon; high fill factor f close to 1 means wehave mostly silicon in the bottom layer (f=1 is an uninterrupted siliconwaveguide in the bottom layer). A low ratio r means much smaller widthtop silicon layer shape than bottom layer shape, r close to 1 meanssimilar width, and r>>1 means top shape is much wider than bottom. Fromthis, we can identify Type B as a design that approaches weak scatteringwhen r goes to 0 and f approaches 1 (see FIG. 19), meaning that we endin a waveguide formed of only the bottom silicon layer. Type A ends in awaveguide comprising both layers with r=1 and f=1 (FIG. 19). Type C endsin a waveguide comprising only the top silicon layer, with r>>1 and fapproaching 0. And, in Type D designs the structure terminates inabsence of silicon in both layers at the weak end of the grating. Thismeans the wave is not guided, and instead the grating couples an out ofplane unguided beam to an in-plane unguided beam. This may also findcertain applications.

In embodiments of the invention, we provide each of the Type A, B, C orD designs, where a grating is synthesized by starting with a desiredbeam distribution, deriving the needed grating strength, using a modeband structure solver to generate scattering strength/directivity mapssuch as in FIGS. 15A, 15E 15B, and 15F, choosing a design type—Type A,B, C, or D depending on desired terminating waveguide type, and readingoff the desired grating strength vs. position from a curve such as FIG.14A (per Dirk Taillaert et al., Optics Letters 2004), selecting fromFIG. 19—depending on the desired design type—the appropriate part of the“high-directivity ridge”, or high directivity region; then finding thedesired scattering strength along the same ridge drawn in FIG. 15E(scattering strength plot), and using those 2 axis parameters (r, f) andtwo other derived parameters (Λ, w_(o)) derived from FIGS. 15G-15H todefine each local unit cell. Repeating the process from left to rightalong the grating a “single shot” synthesis yields a design. Because thetheory that provides this synthesis method is a continuum theory but thestructure comprises discrete unit cells, high (e.g. as high as 95%) butnot 100% coupling efficiencies are typically obtained. Localoptimization or global optimization around this design point can quicklyfurther improve efficiency.

An example can illustrate the synthesis process briefly. Consider thedesired Gaussian beam shape of a particular beam width shown in FIG.14A, with its corresponding desired scattering strength α(x) shown onthe plot as well. Suppose the design maps of the unit cell designutilized are given in FIG. 15, and that we choose a Type A (Normal)design. Then, we start from the input waveguide, and choose a startingpoint on the desired scattering strength curve (e.g. first circle on theleft). In FIG. 15E, we use the top right high directivity ridge toselect a highly directional unit cell, and choose e.g. point A1 whichshows weak scattering strength. Point A1 provides r and f, i.e. wt andwb. Then, point A1 in FIGS. 15G and 15H provides the corresponding Λ andwo. The first unit cell is fully specified. Since it is Λ wide, we goback to our first circle on FIG. 14A, and move a distance Λ to theright, and read off a new value of desired scattering strength for thenext unit cell. The next value requires a stronger scattering so we nowuse e.g. point A2. For a later cell with even stronger scattering we mayuse point A3. This process is repeated until the device is synthesized.Note that in FIG. 14A on the right, some scattering strengths wereunachievable. This affects efficiency but because it happens in theoutskirts of the beam the effect is not large.

Suppose, instead that we chose a Type B Inverted design, the aboveprocess would be the same but we would be using for example points B1 toB3 to select low to high scattering strengths.

This map does not cover the full parameter range for Type C and Ddesigns, but the locations of equivalent C1 to C3 and D1 to D3 pointsare indicated in FIG. 15E.

FIGS. 16A-16E and 17A-17E show example designs. It is exemplified thatthe above procedure produces grating structures that utilizemonotonically changing wt and wb along the grating structure.

For example, in FIG. 16A, starting from the input waveguide, the bottomdevice layer has monotonically decreasing silicon shape widths, and thetop device layer also has monotonically decreasing silicon shape widths.This is consistent with a step by step advance along FIG. 14A indesired/synthesized scattering strength (circles in FIG. 14A), and thesmooth parameter map in FIGS. 15A and 15E for scattering strength alonga high directivity contour and in the high directivity region (see FIGS.15B and 15F for D>10 region and preferably D=100 to above 10000). It istypical of Type A designs to have monotonically decreasing wt and wb inthe same direction. Furthermore, because the input waveguide region hasa high duty cycle of silicon, these designs are efficient if they mateto a bi-layer input waveguide, that is, one formed of both of the devicelayers. A waveguide formed in only one or the other device layerprovides an impedance mismatch, i.e. reflection, at the grating couplerinput, which reduces coupling efficiency. However, bilayer waveguideswhen implemented in device layers formed of crystalline silicon andpolysilicon, as done in the present examples, are lossy becausepolysilicon is is an optically lossy material and attenuates thepropagating wave. Thus, these grating couplers are typically mated to awaveguide taper that tapers down to a single mode waveguide, but alsotransfers light from a two-layer waveguide to a single layer waveguide.In our example, the preferable layer for the waveguide is thecrystalline silicon (low loss) waveguide layer, but in other materialsystems it could be either layer, or both could be utilized. It shouldbe noted that Type A designs typically retain a close to constant wt towb ratio (see FIGS. 15B and 15F). In FIG. 16A, it can be seen thatnarrow oxide gaps next to silicon shapes on the top and bottom layer arenext to the waveguide input on the left, and the silicon shapes narrow(oxide gaps widen) in unison as one moves along the grating design tothe right. In each unit cell, the left wall of a top silicon shape isleft of the left wall of a bottom silicon shape in the same unit cell;and the right wall of the top silicon shape is left of the left wall ofthe bottom silicon shape. The monotonic tapering, however, produces aqualitative difference between the input and middle of the grating suchthat at the input, the top silicon shape overlaps the bottom siliconshape of the next cell to the left (for a downward radiating design),i.e. the left wall of the top silicon shape in a unit cell is to theleft of the right wall of the bottom silicon shape of the unit cell toits left. In the middle of the grating structure, in the region of highstrength scattering, the top silicon shape does not overlap the bottomsilicon shape of adjacent unit cell.

In FIG. 17A, a different design (of Type B) is shown, in which thebottom device layer has monotonically decreasing silicon shape widths,but the top device layer has monotonically increasing silicon shapewidths, starting from the input waveguide. This is consistent with astep by step advance along FIG. 14A in desired/synthesized scatteringstrength (circles in FIG. 14A), and the smooth parameter map in FIGS.15A and 15E for scattering strength along a high directivity contour andin the high directivity region (see FIGS. 15B and 15F for D>10 regionand preferably D=100 to above 10000). For Type B designs, the ratio r ischanging rapidly, the period is not varying rapidly, so as the bottomlayer shapes narrow along the grating, the top ones widen. This designis ideally suited to adiabatically mate, with ideal impedance match, toa single-layer waveguide, in this case in the bottom device layer.Notably, in the first unit cells next to the input waveguide, the toplayer silicon shape is narrower than the bottom shape, and fully withinthe bottom shape (the left wall of the top shape being right of the leftwall of the bottom shape); while to the right of the grating, the shapesalign into high scattering strength directional radiation unit cells,where the top and bottom cell are similar width (if they the devicelayers are of similar thickness as they are here), and the top shape isto the left of the bottom shape, because it is a bottom radiatingdesign. Because it is a bottom radiating design, the top shape is leftof center above the bottom shape, i.e. it is a weak positive scattererin proximity to the oxide gap left of the bottom shape that is a weaknegative scatterer, their proximity creating a quarter-wavelengtheffective spacing, and the whole unit cell being close to a full opticalwavelength or longer if the output radiation is in a forward up or downdirection, away from the input waveguide. For small off normal anglesforward or backward, the unit cell is about a wavelength long (effectivewavelength equal to the free space wavelength divided by the effectiveindex of the Bloch mode propagating in the grating structure). Upradiating designs look similar, but shift the top shapes to the left insuch a way that the first top silicon shape is about the same distanceto the left, rather than to the right, of the first small oxide gap onthe bottom layer at the waveguide input port.

Features of the monotonic tapering of the parameters of unit cells inthe designs in FIG. 16A and FIG. 17A are illustrated in more detail inFIGS. 22A-D and 23A-C. FIG. 22A shows the design in FIG. 16A and showsthe locations of three exemplary unit cells, one at the beginning of thegrating near the input waveguide (FIG. 22B) with weak scattering, asecond point further to the right in the grating cross-section withstronger scattering (FIG. 22C), and a third point in the region ofstrongest scattering (FIG. 22D). FIGS. 22B, 22C and 22D each show a unitcell as well as parts of the adjacent two unit cells to the left andright. In this design the offset wo is weakly changing along thestructure (see points A1,A2,A3 in FIG. 15H), so the top silicon shapeand bottom silicon shape have similar alignment from input through thegrating. The left wall 260 of the top silicon shape is to the left ofthe left wall 258 of the bottom silicon shape, and the right wall 264 ofthe top silicon shape is to the left of the right wall 262 of the bottomsilicon shape in the unit cell. FIG. 22B shows the first unit cell inthe grating of FIGS. 16A and 22A. It is adjacent a bi-layer inputwaveguide 250, 252 having both a polysilicon waveguide part 252 and bodysilicon waveguide part 250, which optimally matches the grating input tothe input waveguide 250,252. The weak scatterers in this case are theoxide gaps between polysilicon shapes in each layer. To provide a highefficiency design, three types of top-to-bottom silicon shape alignmentare utilized in this example. In the weak scatterers, the top siliconshape overlaps the bottom silicon shape of the cell to its left (in thefirst scatter it overlaps the bottom layer part 250 of the inputwaveguide). Hence, in FIG. 22B, the left wall 260 of the top siliconshape is left of the right wall 254 of the bottom layer part 250 of theinput waveguide. In FIG. 22C, for the following unit cells, the leftwall 260 of the top silicon shape of the unit cell is to the left of theright wall 254 of the bottom silicon shape of the unit cell to its left.At a further point in the structure, FIG. 22D shows a high scatteringstrength unit cell, where the top silicon shape does not overlap thebottom silicon shape of the adjacent unit cell. That is, in FIGS. 22D(and 22C) the left wall 260 of the top silicon shape is to the right ofthe right wall 254 of the adjacent unit cell to the left. In certainfabrication processes, any alignment between shapes is permitted. Inother fabrication processes, especially certain unmodified CMOSprocesses, design rules may require a minimum overlap or underlap (i.e.spacing between), so, a minimum spacing between the walls, of a shape inthe top silicon and a shape in the bottom silicon. Such minimum spacingsmay be 50-100 nm, but in advanced processes may be considerably smalleras process nodes advance. In these cases certain unit cell designs maybe disqualified and we may need to use the closest available cell thatmeets design rules. Such rules may be waived in either CMOS or customprocesses to allow ideal implementation of the structures.

FIG. 23A shows the design in FIG. 17A and shows the locations of twoexemplary unit cells, one at the beginning of the grating near the inputwaveguide (FIG. 23B) with weak scattering, and a second point in theregion of strongest scattering (FIG. 22C). In FIG. 23B, we see that adownward output radiation design has produced a small oxide gap in thebottom layer and a small silicon shape in the top layer such that thetop silicon shape is atop the bottom silicon shape in the unit cell andis entirely enclosed by it. That is, the left wall 280 of the topsilicon shape is to the right of the left wall 278 of the bottom siliconshape, while the right wall 284 of the top silicon shape is to the leftof the right wall 282 of the bottom silicon shape. This unit cell matesto a bottom layer only input waveguide 270. On the other hand, at apoint further in the grating, strongly scattering unit cells have thesame design as those of the Type A design in FIGS. 16A and 22A. That is,in FIG. 23C, left wall 280 of the top silicon shape is to the left ofthe left wall 278 of the bottom silicon shape, and the right wall 284 ofthe top silicon shape is to the left of the right wall 282 of the bottomsilicon shape in the unit cell.

An advantage of the Type B design over Type A is as follows. In CMOS SOItechnology, the top layer is poly silicon, which attenuates light. TypeB design has no polysilicon in the input waveguide, and further verylittle polysilicon in the beginning of the grating. Wide top layer, i.e.polysilicon, shapes are introduced only when needed to provide thestrong directional scattering. However, a down side of design Type B(FIG. 17A) relative to Type A (FIG. 16A) is that it may be morerestricted by design rules because walls of top and bottom shapes crossduring the tapering of unit cell parameters along the structure inopposite directions (i.e. top silicon shapes widening and bottom siliconshapes narrowing going from the left to right).

For the purposes of these descriptions, we define a difference in unitcells to refer to a pair of unit cells where at least one cell parameterin a first and a second unit cell has a different value. We definemonotonic variation as an array of at least three unit cells, definingtwo differences in a parameter, for example the width difference betweenunit cell 1 and unit cell 2, and the difference between unit cell 2 andunit cell 3. A monotonic variation in such an array means that thedifference in parameter from one pair of adjacent cells to the next isof the same sign (>0 or <0). In the disclosed grating designs, typicallyat least three, but usually at least a group of several—or all—unitcells have a monotonic variation in at least one parameter. In FIGS.16A-16E and 17A-17E, the wt and wb parameters vary monotonically.

FIGS. 16A-16E shows a Type A (normal) embodiment of the invention. Itshows 95% peak efficiency simulated (92% measured), 99% directivity, and100 nm 3 dB bandwidth. Measured results closely correspond to design.This design is realized in the polysilicon gate and transistor bodylayers of a 45 nm CMOS SOI process with a silicon nitride liner, thenitride appearing as a conformal layer atop the polysilicon layer inFIG. 16A.

FIGS. 17A-17E shows a Type B (inverted) embodiment of the invention. Itshows 88% peak efficiency simulated (84% measured) and 81 nm 3 dBbandwidth. Measured results closely correspond to design. This design isrealized in the polysilicon gate and transistor body layers of a 45 nmCMOS SOI process with a silicon nitride liner, the nitride appearing asa conformal layer atop the polysilicon layer in FIG. 16A).

The following table summarizes the performance of these example designs.“Poly-body interfacing design” refers to the Type A design in FIG.16A-16E. “Body interfacing” design refers to the Type B design in FIG.17A-17E.

TABLE 1 Simulated and experimentally measured performance of exampledesigns Poly-Body-Interfacing Body-Interfacing Simulation ExperimentSimulation Experiment Coupling 95% 92% 88% 84% Efficiency (%) Coupling−0.2 dB −0.36 dB −0.5 dB −0.76 dB Efficiency (dB) 3 dB Bandwidth 100 nm~110 nm 81 nm ~80 nm Wavelength 1201 nm 1197 nm 1206 nm 1178 nm Angle19° 18° 19° 19° Taper Loss (dB) −2.15 dB −0.40 dB Directivity 99% 94%Reflection 0.4%  0.5% 

The Type A and B designs are particularly important for siliconphotonics applications, and those utilizing two silicon device layers.This is because typically a bottom silicon layer can be crystallinesilicon while a top silicon layer is typically polysilicon if the twolayers are independently patternable. The Type B (inverted) design isparticularly important for CMOS SOI applications because it terminatesin the bottom silicon layer, which is crystalline silicon in CMOS SOIand allows low loss waveguides, while the top silicon is polysiliconwhich is typically lossy, having losses typically 50-150 dB/cm. Thegrating is short enough for the optical field to not experiencesignificant loss or. attenuation from the polysilicon, during itspropagation through the coupler, but use of the polysilicon is oftenavoided for waveguiding. Use of the polysilicon within the gratingcoupler structure does not impair coupler efficiency significantly dueto the short length of the coupler. For example, even if polysiliconloss were 100 dB/cm, and duty cycle of use of the polysilicon in thecoupler reduced that effectively to about 50 dB/cm, the typical gratingcoupler length of 10-20 microns means that a signal travels about 10microns on average within the plane of the coupler leading to 50dB/cm×0.001 cm=0.05 dB or 1% loss. Note that the Type B (Inverted)design in FIG. 17A-E shows a unit cell with switched order of scatterersin terms of ordering from the input waveguide port, in comparison to theType A (Normal) design in FIG. 16A-E. That is, in the Type A Normaldesign (designed to radiate down), top and bottom scatterers are oxidegaps, and the top layer oxide gap in each unit cell is closer to theinput waveguide on the left than the bottom layer oxide gap in the samecell. On the other hand, in the Type B Inverted design (designed toradiate down), the top and bottom scatterers are polysilicon bar andoxide gap, respectively. Because of the opposite polarity of scatterer,the order is reversed, with the bottom layer oxide gaps closer to theinput waveguide within each unit cell. Furthermore, in the Type Bdesign, from the input to the grating (on the left in FIGS. 16A-16E or17A-17E) toward the end of the grating (on the right in FIGS. 16A-16E or17A-17E), the top silicon blocks start from small width and become widertoward the end of the grating (right side on the figure), while on thebottom layer they start wide and become narrow toward the end of thegrating. That is, the widths wb and wt are respectively increasing anddecreasing along the length of the coupler. This is a unique anduniversal feature of this design, and will remain so in other similarprocesses, device layer thicknesses, material systems, etc.

Type C Inverted #2 designs mate to an input waveguide on the top layeronly. They could be useful in photonic integrated circuits where, forexample, the top waveguide is a formed in a low-loss high indexdielectric material such as. silicon rich silicon nitride, siliconcarbide, chalcogenide glass, etc., disposed above a crystalline siliconbottom layer, where the bottom Si layer is used to providedirectionality in grating regions, with bottom shapes in silicon and topshapes in the high index dielectric, but the primary waveguide isimplemented in the top layer low-loss dielectric.

A Type C design can be considered to have all the properties of a Type Bdesign when in the Type B design the two device layers including thepatterns on them are interchanged.

Thus in an embodiment of the invention, the top layer silicon widthincreases while the bottom layer silicon width decreases along thegrating. Equivalently, scatterer strengths increase along the grating ifone considers a silicon (positive) scatterer in the top layer, and a gap(negative) scatterer in the bottom layer.

Different approaches can be used that use predetermined changes in widthof silicon to modulate scattering strength including transversesegmentation with different fill factors, as shown in examples in FIGS.6-8. Transverse segmentation has been employed in single-layer gratingcoupler designs to circumvent critical dimension limitations but also tocontrol the scattering strength by means different than controlling thewidth of the bars.

A grating coupler alone, if linear, couples light from an out of planebeam or fiber to a wide input waveguide. It is known in the art thatsuch waveguides can be mated to narrow single mode waveguides usingadiabatic in-plane waveguide tapers which provide mating at low tonegligible cost in optical losses. This approach can connect Type B andC designs to single mode waveguides. It can also connect a Type Agrating coupler design to a single mode waveguide comprising a stack ofpolysilicon and body silicon. Alternatively, a dual taper could bedesigned to transition from a wide waveguide with two silicon layers toa narrow waveguide with a single silicon layer, in order to couple aType A design into a bottom layer, crystalline silicon waveguide only.

The example embodiments described above specify silicon top and bottomlayers, due to their utility in silicon photonics and CMOS processtechnology, but any high index materials could be used for the twolayers. The concepts also work in a uniform background material, or withthe scatterers embedded in a material layer stack (as e.g. shown inexamples in FIGS. 16 and 17).

Changes may be made in the above methods and systems without departingfrom the scope hereof. It should thus be noted that the matter containedin the above description or shown in the accompanying drawings should beinterpreted as illustrative and not in a limiting sense. The followingclaims are intended to cover all generic and specific features describedherein, as well as all statements of the scope of the present method andsystem, which, as a matter of language, might be said to falltherebetween. It is also anticipated that steps of methods may beperformed in an order different from that illustrated and still bewithin the meaning of the claims.

What is claimed is:
 1. A grating coupler configured in a configurationselected from the group consisting of being configured to receive lightof a wavelength from a waveguide and emit a beam, and being configuredto receive light from a beam and emit light of the wavelength throughthe waveguide, the grating coupler comprising: patterned shapes in eachof a first and second layer of planar material and the shapes of atleast the first or the second layer being embedded in backgroundmaterial, a plane defined by the shapes of the first planar materialseparated from a plane defined by the shapes of the second material byless than one wavelength in a direction perpendicular to the planedefined by the shapes of the first planar material; the first and secondlayer of planar material having similar refractive index; a plurality ofadjacent unit cells arranged with a direction of propagation of thelight each comprising a shape of the first material and a shape of thesecond material, each unit cell having design parameters comprising acell width A equal to a distance between a first edge of a shape of thefirst planar material and a first edge of a next shape of the firstplanar material, a width wb of the shape of the first planar material, awidth wt of the shape of the second planar material, and an offsetbetween the first edge of a shape of the first planar material and thefirst edge of the shape of the second material; wherein a directivityratio D of a first and a second unit cell is at least 10 dB; and wherethe first unit cell differs from the second unit cell of the pluralityof unit cells in at least one parameter selected from Λ, wb, wt, andoffset to provide a predetermined beam shape the beam having a directionnot coplanar with the plane defined by shapes of the first materiallayer.
 2. The grating coupler of claim 1 where at least two of theparameters of the first cell differ from corresponding parameters of thesecond cell.
 3. The grating coupler of claim 2 where a wb/wt ratio ofthe first cell is not equal to a wb/wt ratio of the second cell.
 4. Thegrating coupler of claim 3 where the offset of the first cell is notequal to the offset of the second cell.
 5. The grating coupler of claim1 wherein the first unit cell lies near a peak power emissions point ofthe grating.
 6. The grating coupler of claim 1, where the second unitcell is configured to have a radiation strength α that differs from thatof the first unit cell by at least 20%, and the second unit cell alsohas a directionality of at least 10 dB.
 7. The grating coupler of claim1, wherein the second unit cell has a cell width that, when simulated ina uniform periodic grating, produces an output radiation at an anglethat differs from that of the first cell by at least one degree, thecombination of first and second unit cells adapted to produce aconverging beam.
 8. The coupler of claim 1 wherein the first unit cellis closer to the input waveguide than a third unit cell, the third unitcell being closer to the input waveguide than the second unit cell, andthe first unit cell is configured to have an output angle θ1 that leansforward away from the input waveguide and the second unit cell isconfigured to have an output angle θ2 that leans backward, toward theinput waveguide.
 9. A grating coupler configured in a configuration witha waveguide port and a beam port the grating coupler comprising:patterned shapes in a first layer of a first planar material andpatterned shapes in a second layer of a second planar material, theshapes of the first material and the shapes of the second material beingembedded in background material; a plurality of adjacent unit cellsarranged with a direction of propagation of the light each comprising ashape of the first material and a shape of the second material, eachunit cell having design parameters comprising a cell width A equal to adistance between a first edge of a shape of the first planar materialand a first edge of a next shape of the first planar material, a widthwb of the shape of the first planar material, and a width wt of theshape of the second planar material; and where a first unit cell of theunit cells lie closer to the waveguide than a second unit cell of theunit cells and width wt of the shape in the second planar material isgreater in the second unit cell than in the first unit cell.
 10. Thegrating coupler of claim 9, where the unit cells have a monotonicallyincreasing width wt of the shapes in the second planar material from thewaveguide to an end of the coupler distant from the waveguide.
 11. Thegrating coupler of claim 9 wherein the waveguide comprises a shapeformed in the first planar material layer.
 12. The grating coupler ofclaim 9, where the unit cells have a monotonically decreasing width wtof the shapes in the second planar material from the waveguide to adistal terminus of the coupler.
 13. The grating coupler of claim 9wherein the waveguide comprises a shape formed in the second planarmaterial layer.
 14. A method of designing a grating coupler for anoutput angle of interest and a desired beam power distributioncomprising: selecting a center wavelength of operation, a mean outputangle of beam, and a material stack providing a first and a secondpatternable planar device layers where the second patternable devicelayers lies less than the center wavelength above the first patternabledevice layer; determining layer thicknesses and refractive indices ofthe patternable device layers, and at least one refractive index of asurrounding material; using a Bloch Mode Solver with a periodic Blochboundary condition along horizontal axis and radiation absorbingboundaries and a model of a unit cell of the structure for a pluralityof sets of particular choices of parameters, the parameters comprising acell width, a width of a scattering element formed in each of the firstand second patternable layers, and an offset between the scatteringelement in the first patternable layer and the scattering element in thesecond patternable layer at the center wavelength, to provide Blochfield distribution in the unit cell and the complex propagationconstant, extracting from the Bloch field distribution for each set ofparticular choices of parameters an angle θ of emitted radiation, adirectivity D, and an emissions strength α and placing θ, D, and α asentries in a four dimensional table; selecting entries in the fourdimensional table according to the output angle of interest; determiningan approximate desired α for each of a plurality of unit cells in thegrating coupler; finding entries in the four dimensional tablecorresponding to maximal directivity D and desired α for each of theplurality of unit cells.
 15. The grating coupler of claim 6 wherein thefirst and second unit cell lie within a mode field diameter of eachother.